Revisiting the residual temperature distribution in prompt neutron emission in fission

Abstract

A new triangular form of the residual temperature distribution P(T), entering the prompt emission models in which the sequential emission is globally taken into account (e.g., the Los Alamos model of Madland and Nix with subsequent improvements and the Point-by-Point model), is proposed. A deterministic treatment of the successive emission of prompt neutrons, which is based on recursive equations of the residual temperatures, was developed. This modeling was validated by the good description of many and different experimental data of prompt emission (e.g., $\overline{\nu}(A)$ , $\langle\nu\rangle$ (TKE), $\langle\varepsilon\rangle (A)$ , $\langle\varepsilon\rangle$ (TKE), $\overline{E}_{\gamma} (A)$ , etc.) and the good agreement with the results of other prompt emission models. To see a possible systematic behaviour of P(T) as a function of energy and fissioning nucleus, the deterministic treatment of sequential emission was applied to 11 nuclei undergoing fission (spontaneously or induced by thermal and fast neutrons with energies up to the threshold of the second chance fission) for which reliable experimental fission fragment distributions Y(A, TKE) exist. The shapes of all P(T) distributions for the light and heavy fragment groups and for all fragments resulting from this modeling can be approximated with a triangular form. To make possible the use of this form into the prompt emission models with a global treatment of sequential emission, a connection between the average residual temperature $\langle \mathrm{Tr} \rangle$ and the temperature of initial fragments $\langle \mathrm{Ti} \rangle$ is needed. An important finding of this study concerns the ratio $\langle \mathrm{Tr} \rangle / \langle \mathrm{Ti} \rangle$ , which is $ \approx 0.6$ for all studied fissioning systems. This result allows to obtain a new triangular form of P(T) defined only as a function of initial temperature, which is applicable to any fissioning system at any energy, in the frame of prompt emission models with a global treatment of sequential emission.